quantum-cognition

name: quantum-cognition description: > Quantum cognition methodology for modeling cognitive processes using quantum probability theory. Combines neuroscience insights with quantum information formalism to model decision making, context-dependent reasoning, mental state dynamics, and non-classical cognitive correlations. Use when: (1) modeling cognitive phenomena that violate classical probability (order effects, conjunction fallacy), (2) building quantum-like models of decision making, (3) analyzing contextuality in mental representations, (4) designing quantum neural architectures for brain-inspired computing, (5) studying quantum effects in biological systems (radical-pair mechanism, cryptochrome), (6) implementing quantum photonic neural networks for neuromorphic computing.

Quantum Cognition

Model cognitive processes using quantum probability theory and quantum information formalism. This methodology spans two interpretations: quantum-like cognition (informational) and physical quantum brain hypotheses.

Two Paradigms

1. Quantum-Like Cognition (Informational)

Uses quantum formalism to model cognition without claiming quantum processes in the brain. Based on Khrennikov's framework: mental contexts induce non-classical correlations analogous to quantum entanglement. Key insight: incompatible measurements arise naturally from context-dependent mental representations.

When to use: decision making, judgment under uncertainty, concept combinations, cognitive biases, order effects in survey responses.

2. Physical Quantum Brain Hypotheses

Proposes actual quantum coherence in biological substrates. Wakaura (2026) evaluates CQEC (covariant quantum error correction) in radical-pair proteins MAO-A and cryptochrome. Key finding: CQEC can maintain coherence over 200ms behavioral windows, but layer-protein tradeoffs exist — no single protein optimizes all layers.

When to use: biophysical modeling of neural processes, radical-pair mechanism analysis, quantum error correction in biological systems.

Core Mathematical Framework

Quantum Probability Model

Replace classical Kolmogorov probability with quantum probability:

import numpy as np

def quantum_probability(state_vector, projector):
    """P(outcome) = |<outcome|state>|^2 = ||projector @ state||^2"""
    return np.abs(np.dot(projector, state_vector))**2

def interference_effect(p_A, p_B, theta):
    """Classical: p = p_A + p_B
       Quantum: p = p_A + p_B + 2*sqrt(p_A*p_B)*cos(theta)"""
    return p_A + p_B + 2 * np.sqrt(p_A * p_B) * np.cos(theta)

Contextuality Detection

Bell-CHSH inequality violation indicates non-classical correlations:

def chsh_inequality(E_ab, E_ab_prime, E_a_prime_b, E_a_prime_b_prime):
    """|S| = |E(ab) - E(ab') + E(a'b) + E(a'b')| <= 2 (classical)
       Quantum bound: |S| <= 2*sqrt(2) (Tsirelson bound)"""
    S = abs(E_ab - E_ab_prime + E_a_prime_b + E_a_prime_b_prime)
    return S, S > 2.0, S <= 2 * np.sqrt(2)

Cognitive State Evolution

Mental states evolve via unitary transformations (closed system) or Lindblad dynamics (open system):

from scipy.linalg import expm

def mental_state_evolution(H, psi_0, t):
    """|psi(t)> = exp(-iHt)|psi(0)> — unitary evolution"""
    U = expm(-1j * H * t)
    return U @ psi_0

Quantum Photonic Neural Networks (QPNN)

Boras Vazquez et al. (2026): time-bin-encoded QPNN for quantum information processing.

Key architectural insight: time-encoded networks use constant number of photonic elements regardless of size/depth, enabling scaling. Trained via realistic nonlinearities (quantum dot + waveguide) to achieve 0.96+ fidelity Bell-state analysis.

def qpnn_architecture(n_modes, depth, nonlinearity="kerr"):
    """Time-bin QPNN: same elements regardless of network depth.
    Layers: (1) time-delay interferometer, (2) phase shifters,
    (3) nonlinear element (Kerr or quantum dot scattering)"""
    # Each time step processes one mode through same physical elements
    # Complexity: O(n_modes * depth) elements, not O(n_modes * depth) physical components
    return {
        "encoding": "time-bin",
        "elements": "constant with depth",
        "nonlinearity": nonlinearity,
        "fidelity": ">0.96 (realistic), >0.99 (time-gated)"
    }

Quantum Error Correction in Biological Systems

CQEC protocol for radical-pair proteins:

Three-layer architecture: nuclear spin memory → electron spin interface → electrochemistry
Coherence preservation: CQEC extends T2 coherence beyond decoherence rate
Layer-protein tradeoff: CRY has longer T2 (52ms) but shorter T1 (0.53ns); MAO-A has opposite
Behavioral threshold: 200ms Schultze-Kraft veto window is the minimum coherence requirement

Decision Making Patterns

Order Effects

P(A then B) ≠ P(B then A) — classical commutativity violation
Quantum: P(A then B) = ||P_B P_A |psi>||^2 ≠ ||P_A P_B |psi>||^2

Conjunction Fallacy

Linda problem: P(bank teller AND feminist) > P(bank teller) Explained by quantum interference between mental representations.

Disjunction Effect

Violation of sure-thing principle in decision making under uncertainty. Modeled via quantum interference term in probability calculation.

Application Workflow

Identify classical probability violation in cognitive data
Construct quantum state space (Hilbert space dimension = number of distinguishable outcomes)
Define mental state vector and measurement projectors
Fit interference parameters to empirical data
Validate with contextuality tests (Bell-CHSH, Leggett-Garg inequalities)
Predict novel effects (order reversal, compatibility effects)

Key Findings from Literature

CQEC coherence: 0.83 at decoherence rate 0.19 (6.9x improvement over uncorrected)
QPNN fidelity: 0.96 with realistic nonlinearity, 0.99+ with time gating
Contextuality: Mental markers exhibit quantum-like incompatibility without physical quantum processes
Layer tradeoff: No single radical-pair protein optimizes both T1 and T2 coherence times

References

See references/ for detailed mathematical derivations and implementation guides.